Advanced　graph　neural　networks　have　shown　great　potentials　in　graph　classification　tasks　recently.　Different　from　node　classification　where　node　embeddings　aggregated　from　local　neighbors　can　be　directly　used　to　learn　node　labels,　graph　classification　requires　a　hierarchical　accumulation　of　different　levels　of　topological　information　to　generate　discriminative　graph　embeddings.　Still,　how　to　fully　explore　graph　structures　and　formulate　an　effective　graph　classification　pipeline　remains　rudimentary.　In　this　paper,　we　propose　a　novel　graph　neural　network　based　on　supervised　contrastive　learning　with　structure　inference　for　graph　classification.　First,　we　propose　a　data-driven　graph　augmentation　strategy　to　enhance　the　existing　connections.　Concretely,　we　resort　to　a　structure　inference　stage　based　on　diffusion　cascades　to　recover　possible　connections　with　high　node　similarities.　Second,　to　improve　the　contrastive　power　of　graph　neural　networks,　we　propose　a　supervised　contrastive　loss　for　graph　classification.　With　the　integration　of　label　information,　the　one-vs-many　contrastive　learning　is　extended　to　a　many-vs-many　setting.　The　supervised　contrastive　loss　and　structure　inference　can　be　naturally　incorporated　within　the　hierarchical　graph　neural　networks　where　the　topological　patterns　can　be　fully　explored　to　produce　discriminative　graph　embeddings.　Experiment　results　show　the　effectiveness　of　the　proposed　method　compared　with　recent　state-of-the-art　methods.